Abstract
We explore how to study dynamical interactions between brain regions by using functional multilayer networks whose layers represent different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as (i) a multilayer network, in which all brain regions can interact with each other at different frequency bands; and as (ii) a multiplex network, in which interactions between different frequency bands are allowed only within each brain region and not between them. We study the second-smallest eigenvalue λ2 of the combinatorial supra-Laplacian matrix of both the multiplex and multilayer networks, as λ2 has been used previously as an indicator of network synchronizability and as a biomarker for several brain diseases. We show that the heterogeneity of interlayer edge weights and, especially, the fraction of missing edges crucially modify the value of λ2, and we illustrate our results with both synthetic network models and real data obtained from resting-state magnetoencephalography. Our work highlights the differences between using a multiplex approach and a full multilayer approach when studying frequency-based multilayer brain networks.
Highlights
IntroductionDuring the last few years, network science has undergone a conceptual revolution with the extension of well-established techniques of network analysis to multilayer brain networks
We aim to improve the interpretation of algebraic connectivity for functional brain networks, and we investigate (i) how the fact that a considerable fraction of all possible interlayer edges are not present in multiplex networks leads to a deviation from the theoretical values expected for λ2 and (ii) how these deviations are related to the mean weight of the interlayer edges
It is possible to encode such imaging data either as a multiplex network or as a more general type of multilayer network, but different choices lead to different results, which one must interpret from a neuroscientific perspective
Summary
During the last few years, network science has undergone a conceptual revolution with the extension of well-established techniques of network analysis to multilayer brain networks. Multilayer brain network: A brain network with more than one layer. Layers are connected to each other through interlayer edges, which link node-layers from different layers. Node-layer: Within each layer, a node-layer represents the dynamics recorded by a given magnetometer that is filtered at a specific frequency band. Each magnetometer has an associated node-layer on each layer. Layer: A portion of a multilayer network with a particular set of connections (called “intralayer edges”) between nodes. Each layer represents a specific frequency band of a functional brain network
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